Least Common Multiple (LCM) of 40 and 143
The least common multiple (LCM) of 40 and 143 is 5720.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 40 and 143?
First, calculate the GCD of 40 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 143 = 0 remainder 40 |
| 2 | 143 ÷ 40 = 3 remainder 23 |
| 3 | 40 ÷ 23 = 1 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 86 | 3010 |
| 23 and 17 | 391 |
| 67 and 168 | 11256 |
| 69 and 31 | 2139 |
| 80 and 129 | 10320 |